CHAPTER THIRD.

OF THE ARISTOTELIAN LOGIC.

SECTION I.

Of the Demonstrations of the Syllogistic Rules given by Aristotle and his Commen

tators.

THE great variety of speculations which, in the present state of science, the Aristotelian logic naturally suggests to a philosophical inquirer, lays me, in this chapter, under the necessity of selecting a few leading questions, bearing immediately upon the particular objects which ĺ have in view. In treating of these, I must, of course, suppose my readers to possess some previous acquaintance with the subject to which they relate ; but it is only such a general knowledge of its outlines and phraseology, as, in all universities, is justly considered as an essential acccomplishment to those who receive a liberal education.

I begin with examining the pretensions of the Aristotelian logic to that pre-eminent rank which it claims among the sciences; professing, not only to rest all its conclusions on the immoveable basis of demonstration, but to have reared this mighty fabric on the narrow groundwork of a single axiom. "On the basis," says the latest of his commentators, " of one simple truth, Aristotle has reared a lofty and various structure of abstract science, clearly expressed and fully demonstrated."* Nor have these claims been disputed by mathematicians themselves. "In logicâ," says Dr. Wallis, "structura syllogismi demonstratione nititur pure mathematicâ." And, in another passage: "Sequitur institutio logica, communi usui áccommodata.-Quo videant tirones, syllogis

morum leges strictissimis demonstrationibus plane mathematicis ita fundatas, ut consequentias habeant irrefragabiles, quæque offuciis fallaciisque detegendis sint accommodatæ."* Dr. Reid, too, although he cannot be justly charged, on the whole, with any undue reverence for the authority of Aristotle, has yet, upon one occasion, spoken of his demonstrations with much more respect than they appear to me entitled to. "I believe,” says he, "it will be difficult, in any science, to find so large a system of truths of so very abstract and so general a nature, all fortified by demonstration, and all invented and perfected by one man. It shows a force of genius, and labor of investigation, equal to the most arduous attempts." +

As the fact which is so confidently assumed in these passages would, if admitted, completely overturn all I have hitherto said concerning the nature both of axioms and of demonstrative evidence, the observations which follow seem to form a necessary sequel to some of the preceding discussions. I acknowledge, at the same time, that my chief motive for introducing them, was a wish to counteract the effect of those triumphant panegyrics upon Aristotle's Organon, which of late have been pronounced by some writers, whose talents and learning justly add much weight to their literary opinions; and an anxiety to guard the rising generation against a waste of time and attention, upon a study so little fitted, in my judgment, to reward their labor.

The first remark which I have to offer upon Aristotle's demonstrations, is, That they proceed on the obviously false supposition of its being possible to add to the conclusiveness and authority of demonstrative evidence. One of the most remarkable circumstances which distinguishes this from that species of evidence which is commonly called moral or p

ceptible of degrees; the process of reasoning of which it is the result, being either good for nothing, or so perfect and complete in itself, as not to admit of support from any adventitious aid. Every such process of reasoning, it is well known, may be resolved into a series of legitimate syllogisms, exhibiting separately and distinctly, in a light as clear and strong as language can afford, each successive link of the demonstration. How far this conduces to render the demonstration more convincing than it was before, is not now the question. Some doubts may reasonably be entertained upon this head, when it is considered, that, among the various expedients employed by mathematical teachers to assist the apprehension of their pupils, none of them have ever thought of resolving a demonstration (as may always be easily done) into the syllogisms of which it is composed.* But, abstracting altogether from this consideration, and granting that a demonstration may be rendered more manifest and satisfactory by being syllogistically stated; upon what principle can it be supposed possible, after the demonstration has been thus analysed and expanded, to enforce and corroborate, by any subsidiary reasoning, that irresistible conviction which demonstration necessarily commands?

It furnishes no valid reply to this objection, to allege, that mathematicians often employ themselves in inventing different demonstrations of the same theorem; for, in such instances, their attempts do not proceed from any anxiety to swell the mass of evidence, by finding (as in some other sciences) a variety of collateral arguments, all bearing, with their combined force, on the

From a passage, indeed, in a memoir by Leibnitz, (printed in the sixth volume of the Acta Eruditorum) it would seem, that a commentary of this kind on the first six books of Euclid, had been actually carried into execution by two writers, whose names he mentions. "Firma autem demonstratio est, quæ præscriptam a logicâ formam servat, non quasi semper ordinatis scholarum more syllogismis opus sit (quales Christianus Herlinus et Conradus Dasypodius in sex priores Euclidis libros hibuerunted ita saltem ut argumentatio concludat vi formæ," &c. &c.-Acta 1. I. p. 285. Venet. 1740.

r of the works alluded to in the above sentence; and, upon hould scarcely have conceived it to be credible, that any Euclid, had ever seriously engaged in such an ifficult to devise a more effectual expedient for the futility of the syllogistic theory.

same truth;-their only wish is, to discover the easiest and shortest road by which the truth may be reached. In point of simplicity, and of what geometers call elegance, these various demonstrations may differ widely from each other; but, in point of sound logic, they are all precisely on the same footing. Each of them shines with its own intrinsic light alone; and the first which occurs (provided they be all equally understood) commands the assent not less irresistibly than the last.

The idea, however, on which Aristotle proceeded, in attempting to fortify one demonstration by another, bears no analogy whatever to the practice of mathematicians in multiplying proofs of the same theorem; nor can it derive the slightest countenance from their example. His object was not to teach us how to demonstrate the same thing in a variety of different ways; but to demonstrate, by abstract reasoning, the conclusiveness of demonstration. By what means he set about the accomplishment of his purpose, will afterwards appear. At present, I speak only of his design; which, if the foregoing remarks be just, it will not be easy to reconcile with correct views, either concerning the nature of evidence, or the theory of the human understanding.

For the sake of those who have not previously turned their attention to Aristotle's Logic, it is necessary, before proceeding farther, to take notice of a peculiarity (and, as appears to me, an impropriety) in the use which he makes of the epithets demonstrative and dialectical, to mark the distinction between the two great classes into which he divides syllogisms; a mode of speaking which, according to the common use of language, would seem to imply, that one species of syllogisms may be more conclusive and cogent than another. That this is not the case, is almost self-evident; for, if a syllogism be perfect in form, it must, of necessity, be not only conclusive, but demonsly conclusive. Nor is this, in fact, the idea which tle himself annexed to the distinction; for he tell to the form of syllogisms, bu plainer language, to the degree

ing the premises on which they proceed.* In the two books of his last Analytics, accordingly, he treats of syllogisms which are said to be demonstrative, because their premises are certain; and in his Topics, of what he calls dialectical syllogisms, because their premises are only probable. Would it not have been a clearer and juster mode of stating this distinction, to have applied the epithets demonstrative and dialectical to the truth of the conclusions resulting from these two classes of syllogisms instead of applying them to the syllogisms themselves? The phrase demonstrative syllogism certainly seems, at first sight, to express rather the complete and necessary connexion between the conclusion and the premises, than the certainty or the necessity of the truths which the premises assume.

To this observation it may be added, (in order to prevent any misapprehensions from the ambiguity of language,) that Aristotle's idea of the nature of demonstration, is essentially different from that which I have already endeavoured to explain. "In all demonstration," says Dr. Gillies, who, in this instance, has very accurately and clearly stated his author's doctrine, "the first principles must be necessary, immutable, and therefore eternal truths, because those qualities could not belong to the conclusion, unless they belonged to the premises, which are its causes." According to the †

To the same purpose also Dr. Wallis: " Syllogismus Topicus (qui et Dialecticus dici solet) talis haberi solet syllogismus (seu syllogismorum series) qui firmam potius præsumptionem, seu opinionem valde probabilem creat, quam absolutam certitudinem. Non quidem ratione Forme, (nam syllogismi omnes, si in justâ formâ, sunt demonstrativi; hoc est, si præmissæ veræ sint, vera erit et conclusio,) sed ratione Materiæ, seu Præmissarum; quæ ipsæ, utplurimum, non sunt absolute certæ, et universaliter veræ ; sed saltem probabiles, atque utplurimum veræ."- Wallis, Logica, Lib. iii. cap. 23.

Aristotle's Ethics and Politics, &c. By Dr. Gillies. Vol I. p. 96.

I am much at a loss how to reconcile this account of demonstrative evidence with the view which is given by Dr. Gillies of the nature of syllogism, and of the principles on which the syllogistic theory is founded. In one passage (p. 81.) he tells us, that "Aristotle invented the syllogism, to prevent imposition arising from the abuse of words;" in a second, (p. 83.) that "the simple truth on which Aristotle has reared a lofty and various structure of abstract science, clearly expressed and fully demonstrated is itself founded in the natural and universal texture of language: in a third, (p. 86.) that "the doctrines of Aristotle's Organon have been strangely perplexed by confounding the grammatical principles on which that work is built mallest axioms." Is it possible, to suppose, that Aristotle could have

crammatical principles,-to truths founded in the ouage-the epithets of necessary, immutable,

rwise it might be easily shown, how